10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The system of equations \[ax+3y=1,\] \[-12x+ay=2\] has.......... for all real values of

A) no solution

B) unique solution

C) infinitely many solution

D) None of these

Correct Answer: B

Solution :

[b] Given, \[ax+3y=1\]and \[-12x+ay=2\]

Here, \[{{a}_{1}}=a,\,\,\,{{b}_{1}}=3,\,\,{{c}_{1}}=1\]

and \[{{a}_{2}}=-12,\,{{b}_{2}}=a,\,\,{{c}_{2}}=2\]

Now, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{a}{-12},\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{3}{a}\]and \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{1}{2}\]

Condition for unique solution,

\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\Rightarrow \frac{a}{-12}\ne \frac{3}{a}\Rightarrow {{a}^{2}}\ne -36\]

So, the given equations has unique solution for all real values of a.